One type of temperature sensor can typically consist of two SAW resonators denoted R1 and R2 and undertake differential measurements. For this purpose the two resonators are designed to have different resonant frequencies.
Typically, each resonator is composed of a transducer with inter-digitated combs, consisting of an alternation of electrodes, which are repeated with a certain periodicity called the metallization period, deposited on a piezoelectric substrate that may advantageously be quartz. The electrodes, advantageously aluminium or aluminium alloy (produced by a photolithography method), exhibit a low thickness relative to the metallization period (typically, a few hundred nanometers to a few micrometers). For example for a sensor operating at 433 MHz, the metal (aluminium for example) thickness used can be of the order of 100 to 300 nanometers, the metallization period and the electrode width possibly being respectively of the order of 3.5 μm and 2.5 μm.
One of the ports of the transducer is for example linked to the live point of a Radio Frequency (RF) antenna and the other to earth or else the two ports are linked to the antenna if the latter is symmetric (dipole for example). The field lines thus created between two electrodes of different polarities give rise to surface acoustic waves in the zone of overlap of the electrodes.
The transducer is a bi-directional structure, that is to say the energy radiated towards the right and the energy radiated towards the left have the same intensity. By arranging electrodes on either side of the transducer, the said electrodes playing the role of reflector, a resonator is produced, each reflector partially reflecting the energy emitted by the transducer.
If the number of reflectors is multiplied, a resonant cavity is created, characterized by a certain resonant frequency. This frequency depends firstly on the speed of propagation of the waves under the network, the said speed depending mainly on the physical state of the substrate, and therefore sensitive for example to temperature. In this case, this is the parameter which is measured by the interrogation system and it is on the basis of this measurement that a temperature can be calculated.
It is recalled that the variation of the resonant frequency as a function of temperature of a quartz resonator is determined by the following formula:f(T)=f0[1+CTF1(T−T0)+CTF2(T−T0)2]                With f0 the frequency at T0, T0 being the reference temperature (25° C. by convention), CTF1 the first-order coefficient (ppm/° C.) and CTF2 the second-order coefficient (ppb/° C.2).        
The two resonators can use different wave propagation directions, produced though an inclination of the different inter-digitated electrode combs on one and the same substrate, for example quartz.
The two resonators can also advantageously use different quartz cuts making it possible to endow them with different resonant frequencies, in this instance for the resonator R1 the quartz cut (YX1)/θ1 and for the resonator R2: the cut (YX1)/θ2 with reference to the IEEE standard explained hereinafter, the two resonators using propagation which is collinear with the crystallographic axis X.
Whatever solution is adopted for creating different resonant frequencies, the fact of using a differential structure presents several advantages. The first is that the frequency difference of the resonators is almost linear as a function of temperature and the residual non-linearities taken into account by the calibration of the sensor. Another advantage of the differential structure resides in the fact that it is possible to sidestep the major part of the ageing effects.
It is recalled that the expression “calibration operation” denotes the determination of so-called calibration parameters A0, A1 and A2 of the following function:T=A0±√{square root over (A1+A2Δf)}
When these parameters are defined, a differential measurement of frequency then makes it possible to determine a temperature.
Generally, resonators are produced collectively on wafers 100 mm in diameter, typically this might involve fabricating about 1000 specimens on one and the same wafer. This therefore gives 1000 specimens of resonators R1 and 1000 specimens of resonators R2, each temperature sensor comprising a pair of resonators R1 and R2.
The calibration operation is nonetheless expensive in terms of time since it makes it necessary to measure for each sensor the frequency difference between the two resonators at three different temperatures at the minimum and moreover requires the serialization of each sensor (corresponding to the identification of a sensor—calibration coefficients pair for each sensor).
It is for example possible to envisage storing the calibration coefficients A0, A1, A2 in the interrogation system. This configuration requires, in the event of a change of sensor, that the new coefficients be stored in the interrogation system.
One of the aims sought in the present invention is to produce a calibration-free temperature sensor while retaining good precision in the temperature measurement.
For this purpose it is necessary to control on the one hand the dispersion in the difference in resonant frequencies of the resonators R1 and R2, and on the other hand the dispersion in the coefficients CTF1 and CTF2 (first-order and second-order temperature coefficients), or at least the difference in these coefficients CTF1 and CTF2 when a differential measurement is carried out, as is demonstrated hereinafter and by virtue of the following various reminders:
1) Concerning Crystalline Orientation
In order to define the crystalline orientations, the IEEE standard is used. This designation uses the following 2 reference frames:                the crystallographic reference frame (X, Y, Z).        the working reference frame (w, l, t) defined by the surface of the substrate (normal to {right arrow over (t)}) and the direction of propagation of the surface waves (axis {right arrow over (l)}).        
The designation of a cut is of the type (YX wlt)/φ/θ/ψ with:                YX two crystalline axes making it possible to place the working reference frame with respect to the crystallographic reference frame before any rotation. The first axis is along the axis t, normal to the surface whereas the second is along the axis l. The third axis of the working reference frame w is given by the sense of the right-handed trihedron (w, l, t).        w, l, t indicates a series of axes around which it is possible to perform successive rotations by respective angles φ, θ, ψ. In the subsequent description, the variables φ, θ, ψ are associated with rotations around the respective axes w, l, t.        
2) Concerning the Geometry of the Saw Resonator:
The dimensions characterizing a surface wave device consisting of inter-digitated electrode combs Ei, which are symmetric with respect to an axis Ac and deposited on the surface of a piezoelectric substrate are denoted in the following manner and illustrated in FIG. 1:
the metallization period denoted: “p”;
the wavelength denoted: “λ”, with λ=2·p;
the electrode width denoted: “a”;
the metallization thickness denoted “h”.
In general, to sidestep the operating frequency of the device, the following normalized variables are actually used:                the metallization ratio a/p, ratio of electrode width to the metallization period;        the normalized metallization thickness h/λ ratio of the metallization thickness to the wavelength λ=2·p.        
3) Concerning the Laws of Variations with Temperature of 2 Surface Wave Resonators:
As defined previously it is possible to express the frequency behaviours of the two resonators respectively by the following equations:For the resonator R1: f1(T)=f01·(1+C11·(T−T0)+C21·(T−T0)2)  (1)
With: f1(T) the resonant frequency of R1 as a function of temperature
f01 the resonant frequency of R1 at the temperature T0 (generally 25° C.);
C11 the 1st-order temperature coefficient (generally called CTF1) of R1;
C21 the 2nd-order temperature coefficient (generally called CTF2) of R1;For the resonator R2: f2(T)=f02·(1+C12·(T−T0)+C22·(T−T0)2)  (2)
With: f2(T) the resonant frequency of R2 as a function of temperature
f02 the resonant frequency of R2 at the temperature T0 (generally 25° C.);
C12 the 1st-order temperature coefficient (generally called CTF1) of R2;
C22 the 2nd-order temperature coefficient (generally called CTF2) of R2;
In the general case, the resonant frequency at 25° C. and the 1st-order and 2nd-order temperature coefficients depend mainly:
on the chosen crystalline orientation;
on the metallization period of “p” for f0 alone;
on the normalized metallization thickness h/λ;
on the metallization ratio a/p.
And generally, the frequency difference is a function of temperature which can therefore be expressed in the following manner:
                                                                        Δ                ⁢                                                                  ⁢                                  f                  ⁡                                      (                    T                    )                                                              =                            ⁢                                                                    f                    2                                    ⁡                                      (                    T                    )                                                  -                                                      f                    1                                    ⁡                                      (                    T                    )                                                                                                                          =                            ⁢                                                f                  02                                -                                  f                  01                                +                                                      (                                                                                                                                                                                      C                                12                                                            ·                                                              f                                02                                                                                      -                                                                                                                                                                                                          C                              11                                                        ·                                                          f                              01                                                                                                                                            )                                    ·                                      (                                          T                      -                                              T                        0                                                              )                                                  +                                                                                                      ⁢                                                (                                                                                                                                                                        C                              22                                                        ·                                                          f                              02                                                                                -                                                                                                                                                                                          C                            21                                                    ·                                                      f                            01                                                                                                                                )                                ·                                                      (                                          T                      -                                              T                        0                                                              )                                    2                                                                                                        =                            ⁢                                                Δ                  0                                +                                  s                  ·                                      (                                          T                      -                                              T                        0                                                              )                                                  +                                  ɛ                  ·                                                            (                                              T                        -                                                  T                          0                                                                    )                                        2                                                                                                          (        3        )            
With: Δ0=f02−f01 the difference in resonant frequency at the temperature T0;
s=C12·f02−C11·f01 the 1st-order differential coefficient
ε=C22·f02−C21·f01 the 2nd-order differential coefficient
The calibration coefficients make it possible on the basis of a measurement of the frequency difference to get back to the temperature information. It can be shown that:
                    T        =                                            T              0                        +                                                            -                  s                                ±                                                                            s                      2                                        -                                          4                      ⁢                                              ɛ                        ⁡                                                  (                                                                                    Δ                              0                                                        -                                                          Δ                              ⁢                                                                                                                          ⁢                              f                                                                                )                                                                                                                                                2                ⁢                ɛ                                              =                                    A              0                        ±                                                            A                  1                                +                                                      A                    2                                    ⁢                  Δ                  ⁢                                                                          ⁢                  f                                                                                        (        4        )            
Where A0, A1 and A2 are the calibration coefficients as explained in the preamble of the present description.
4) Concerning Manufacturing Dispersions:
The methods of fabrication of resonators being controlled with a certain precision, the crystalline orientation (φ, θ, ψ) and the geometry of the resonator (related to the parameters a and h alone, in effect it is considered that the metallization period p is perfectly controlled) are never, in practice, exactly those aimed at and moreover they are not perfectly reproducible.
For a sufficiently large sample, these parameters follow Gaussian distributions (law of large numbers) whose means and standard deviations can be determined experimentally. The whole set of variations of the five parameters φ, θ, ψ, a and h is called manufacturing dispersions.
The parameters f0, C11, C12 and C21, C22 being dependent on φ, θ, ψ, a and h, can also be controlled with a certain precision and can follow distributions centred around a mean with a certain standard deviation.
The applicant has started from the assumption that there were three predominant parameters in terms of manufacturing dispersions with respect to the set of five parameters f0, C11, C12 and C21, C22.
The three predominant parameters in the manufacturing dispersions are the following:                the dispersion in the angle of cut θ which corresponds in IEEE notation to the cut (YX1)/θ;        the dispersion in the metallization thickness a;        the dispersion in the electrode width h.        
Indeed, the cuts of the substrates are chosen such that they comply with the criteria: φ=0 and ψ=0 thereby corresponding to the crystalline orientation (YXwlt)/φ=0/ψ=0 in IEEE notation.
Now, the points φ=0 and ψ=0 correspond to points at which all the derivatives with respect to φ and ψ vanish. The variations of the following parameters taken into account (f0, C1, C2) can be considered zero around these points:
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ∂                                                                                                                  f                                                          0                                                                                                                                                                                                                            ∂                                                        φ                                                                                                                                                                                                                                                                                                                      φ                                                    =                                                    0                                                                                                                                                  =                                                0                                                                                            ⁢                                                                                                                                                                                          ⁢                                                                                                                                                ∂                                                                                                      C                                                    1                                                                                                                                                                                                    ∂                                                  φ                                                                                                                                                                                                                                                                                                                      φ                                            =                                            0                                                                                                                          =                                        0                                                                            ⁢                                                                                                                                                          ⁢                                                                                                                        ∂                                                                                      C                                            2                                                                                                                                                                    ∂                                          φ                                                                                                                                                                                                                                                              φ                                    =                                    0                                                                                                  =                                0                                                            ⁢                                                                                                                          ⁢                                                                                                ∂                                                                      f                                    0                                                                                                                                    ∂                                  ψ                                                                                                                                                                                                      ψ                            =                            0                                                                          =                        0                                            ⁢                                                                                          ⁢                                                                        ∂                                                      C                            1                                                                                                    ∂                          ψ                                                                                                                                              ψ                    =                    0                                                  =                0                            ⁢                                                          ⁢                                                ∂                                      C                    2                                                                    ∂                  ψ                                                                                      ψ            =            0                          =        0                            (        5        )            
Typically and by way of example, the following dispersions in these 3 parameters can be considered:
a dispersion in electrode width: Δa=+/−0.06 μm;
a dispersion in metallization thickness: Δh=+/−30 Angströms;
a dispersion in angle of cut: Δθ=+/−0.05°.
Assuming the 3 parameters follow Gaussian distributions, +/−3 times the standard deviation of the relevant parameter is called the dispersion:
Δa=+/−3·σ(a)
Δh=+/−3·σ(h)
Δθ=+/−3·σ(θ)
With σ(a), σ(h), σ(θ) respectively the standard deviations of the electrode width a, of the metallization thickness h and of the angle of cut θ.
Note that for a Gaussian distribution with mean μ and standard deviation σ, 99.74% of the most probable population is in the interval [μ−3·σ, μ+3·σ]:P(μ−3·σ<X<μ+3·σ)=0.9974  (6)
In the subsequent description, the expression “nominal value” refers to the values of the parameter a, h or θ aimed at during fabrication and called hereinafter: anom, hnom, θnom.
Moreover, for each of the 3 parameters, the following cases are considered:amin=anom−Δa amax=anom+Δa hmin=hnom−Δh hmax=hnom+Δh θmin=θnom−Δθ θmax=θnom+Δθ  (7)
5) Concerning the Sensor Calibration Operation:
The parameters f0, C1, C2 controlled with a certain precision, are distributed according to a distribution centred around a mean with a certain standard deviation. The laws of variations with temperature of the resonators are therefore not identical for all the sensors and the same holds for the calibration coefficients.
To obtain maximum precision of temperature measurement, the calibration coefficients must therefore be calculated individually for each sensor. For this purpose, it is necessary to measure Δf(T) over the whole of the temperature span where the sensor is used so as to fit the coefficients Δ0, s, ε and ultimately calculate A0, A1 and A2.
This operation is very lengthy and hardly compatible with high-volume production, one seeks therefore to sidestep it.
Among the solutions that may be conceived for accomplishing collective fabrication of calibration-free SAW sensors it is conceivable to use a suite of common calibration coefficients for a set of sensors while maintaining acceptable measurement precision. Moreover, a limited number of sensors can be measured temperature-wise (representative sample) making it possible to determine a mean calibration coefficients suite used for the whole set of sensors. It is then advisable that a suite of calibration coefficients should be common to the largest possible number of sensors, the ideal even being that a suite of coefficients should be common to all the sensors of a given type (defined by the crystalline orientation and the geometry of each of the 2 resonators). This therefore produces what is called a “calibration-free sensor”.
Generally, by considering the law of differential variations with temperature, given by expression (3), it is seen that it is necessary to reduce the dispersions in Δ0, s and ε, if one wishes to have a suite of common calibration coefficients for all the sensors, while having good precision of frequency measurement.
One solution is to reduce the dispersions in f01, C11, C21, f02, C12 and C22. This leads to carrying out a sorting operation on each of the 3 parameters of the two resonators. This approach is, however, not that adopted in the present invention for the following reasons:                one of the objectives is to not measure the sensors temperature-wise individually, therefore the values of C11, C21, C12 and C22 are not known for each sensor.        moreover, calculations have shown that a sorting operation such as presented reduces the yields too much if acceptable measurement precision is desired.        